## PD Peter Massopust, Ph.D.

PrivatdozentTechnische Universität München

Zentrum Mathematik - M15

Boltzmannstraße 3

85748 Garching Room: 02.10.038

Phone: +49-89-289-17488

eMail: massopustma.tum.de

## News

I was awarded a GIAN lectureship under the GIAN initiative (Global Initiative of Academic Networks^{}). The lecturship is comprised of a two-week long lecture series on "Splines and Fractals in Approximation and Interpolation Theory" and will be held at IIT Madras, India, from July 15 - 31, 2016.

## Research Interests

- Efficient Representations of Multidimensional Data via Frames, Wavelets, and Fractals
- Abstract and Applied Harmonic Analysis
- Functional Analysis
- Wavelets, Splines, and Frames
- Approximation and Interpolation Theory
- Fractal Analysis and Fractal Geometry

## Recently Organized Conferences and Workshops

- Symposium on Higher-dimensional Splines: Variations on a Theme
^{}, ICNAAM 2014, September 22 - 28, 2014, Rhodes, Greece (with Patrick Van Fleet, University of St. Thomas, St. Paul, Minnesota, USA) - SampTA 2013
^{}, July 1 - 5, 2013 at the Jacobs University, Bremen, Germany (with Götz Pfander, Werner Henkel, Peter Oswald, Jacobs University Bremen, Peter Maaß, University of Bremen, Holger Rauhut, RWTH Aachen) - Summer School on New Trends and Directions in Harmonic Analysis, Fractional Operator Theory and Image Analysis, Sept. 17 - 22, 2012 in Inzell, Germany (with Brigitte Forster, Universität Passau)

## Recent Publications (last ten years)

### Monographs

- P. Massopust, Fractal Functions, Fractal Surfaces, and Wavelets, Academic Press, 2nd ed., 426 pp., August 2016.

### Text books

- P. Massopust, Interpolation and Approximation with Splines and Fractals
^{}, Oxford University Press, 336 pp., Jan. 2010. - B. Forster and P. Massopust, Eds., Contributors: O. Christensen, K. Gröchenig, D. Labate, P. Vandergheynst, G. Weiss, Y. Wiaux, Four Short Courses in Harmonic Analysis
^{}, Applied and Numerical Harmonic Analysis (ANHA), Birkhäuser Verlag , approx. 250 pp., Nov. 2009.

### Edited books

- D. Larson, P. Massopust, M. Nguyen, M. Papadakis, Z. Nashed, and A. Zayed, eds.,
*Frames and Operator Theory in Analysis and Signal Processing,*Contemporary Mathematics, AMS Book Series, Vol. 451, 291 pp., 2008. - E. Grinberg, D. Larson, P. Massopust, P.E.T. Jorgensen, G. Olafsson, E.T. Quinto, and B. Rubin, eds.,
*Radon Transforms, Geometry, and Wavelets,*Contemporary Mathematics, AMS Book Series, 2008.

### Special Issues Edited

- Numerical Functional Analysis and Optimization: Special Issue on Operator Algebras and Representation Theory: Frames, Wavelets, and Fractals, Vol. 33, Issue 7--9, 2012 (with P. G. Casazza, Palle E. T. Jorgensen, Keri A. Kornelson, Gitta Kutyniok, David R. Larson, Gestur \'{O}lafsson, Judith A. Packer, Sergei D. Silvestrov and Qiyu Sun).
- Sampling Theory in Signal and Image Processing: Special Issue SampTA 2013, Proceedings of the International Conference on Sampling Theory and its Applications held at Jacobs-University Bremen, Germany, Vol. 13, Nos. 1--4, 2014 (with Götz Pfander and Holger Rauhut).

### Journal Articles

- J. Hogan and P. Massopust, Quaternionic B-Splines, submitted 2016.
- P. Massopust, B. Forster and O. Christensen, Fractional and Complex Pseudo-Splines and the Construction of Parseval Frames, submitted 2016, http://arxiv.org /abs/1602.08580.
- P. Massopust, Local Fractal Interpolation on Unbounded Domains, to appear Proceedings of the Edinburgh Mathematics Society.
- A. Schindele, B. Forster, and P. Massopust, Multigrid Convergence for the MDCA-Curvature Estimator, to appear Journal of Mathematical Imaging and Vision.
- P. Massopust and P. Van Fleet, Fractional Cone and Hex Splines, to appear Rocky Mountain Journal of Mathematics, http://arxiv.org/abs/1504.00546.
- M. Storath, L. Demaret, and P. Massopust, Signal Analysis Based on Complex Wavelet Signs, to appear in Applied and Computational Harmonic Analysis.
- K. Hahn, P. Massopust and S. Prigarin, A new method to measure complexity in binary or weighted networks and applications to functional connectivity in the human brain, BMC Bioinformatics.2016, 17:87.
- P. Massopust, Local Fractal Functions in Besov and Triebel-Lizorkin Spaces, J. Math. Anal. Appl., 436 (2016), 393 - 407.
- P. Massopust and Ahmed I. Zayed, On the Invalidity of Fourier Series Expansions of Fractional Order, Fract. Calc. Appl. Anal., Vol. 18, No 6 (2015), 1507 - 1517.
- P. Massopust, Fractal Hypersurfaces, Wavelet Sets, and Affine Weyl Groups, Lecture Notes for Invited Presentations at the International Conference on Fractals, Wavelets and their Applications, Kerala, India, 2013.
- O. Christensen, B. Forster, and P. Massopust, Directional time frequency analysis via continuous frames, Bull. Aust.Math. Soc., 92 (2015), 268 - 281.
- P. Massopust, On local fractal functions in Banach spaces, AIP Conf. Proc. 1684 (2015), 64002-01 - 64002-04.
- M. F. Barnsley and P. Massopust, Bilinear Fractal Interpolation and Box Dimension, Journal of Approximation Theory, 192 (2015), 363 - 378.
- P. Massopust, Fractional Operators, Dirichlet Averages, and Splines, Applied and Numerical Harmonic Analysis: New Perspectives on Approximation and Sampling Theory (Festschrift in Honor of Paul Butzer's 85th Birthday) (2014), 399 - 422.
- P. Massopust, Exponential Splines of Complex Order, Contemporary Mathematics, Vol. 626 (2014), 87 - 106.
- P. Massopust, Local Fractal Functions and Function Spaces, Springer Proceedings in Mathematics & Statistics: Fractals, Wavelets, and their Applications, Vol. 92(2014), 245 - 270.
- M. F. Barnsley, M. Hegland, P. Massopust, Numerics and Fractals, Bulletin of the Institute of Mathematics, Academica Sinica (N.S.), Vol. 9(3)(2014), 389 - 430.
- M. Storath, L. Demaret and P. Massopust, Wavelet Signs: A New Tool for Signal Analysis, Proceedings of the 10th International Conference on Sampling Theory and Applications, EUROSIP, (2013), 45 - 48.
- B. Forster, R. Garunkstis, P. Massopust, and J. Steuding, Complex B-Splines and Hurwitz Zeta Functions, London Math. Soc. Journal of Computation and Mathematics 16(2013), 61 - 77.
- O. Christensen and P. Massopust, Exponential B-splines and the partition of unity property, Advances in Computational Mathematics 37(3)(2012), 301 - 318.
- P. Massopust, Splines of Complex Order: An Introduction, AIP Conference Proceedings, Vol. 1479 (2012), 991 - 994.
- B. Forster, P. Massopust and T. Übelacker, Periodic splines of complex order, Numerical Functional Analysis and Optimization, 33 (7 - 9)(2012), 989 - 1004.
- P. Massopust, Moments of Complex B-Splines, Commun. Math. Anal., Vol. 12, Number 2 (2012), 58 - 70.
- B. Forster and P. Massopust, Short Communication: Multivariate Interpolation with Fundamental Splines of Fractional Order, Proc. Appl. Math. Mech. Vol. 11 (2011), 857 - 858.
- B. Forster and P. Massopust, Splines of Complex order: Fourier, Filters, and Fractional Derivatives, Sampling Theory in Signal and Image Processing, Vol. 10, No. 1-2 (2011), 89 - 109.
- B. Forster and P. Massopust, Interpolation with fundamental splines of fractional order, Proceedings of SampTA 2011.
- S. Held, M. Storath, P. Massopust, and B. Forster, Steerable wavelet frames based on the Riesz transform,
^{}IEEE Transactions on Image Processing, Volume 19, Issue 3 (2010), 653 - 667. - D. Larson, P. Massopust, and G. Olafsson, Three-way Tiling Sets in Two Dimensions, Acta Applicandae Mathematicae, 108 (2010), 529 - 546.
- P. Massopust and B. Forster, Multivariate Complex B-splines and Dirichlet Averages, J. Approx. Theory 162 (2010), 252 - 269.
- B. Forster and P. Massopust, Mathematical Aspects of Time Frequency Analysis, in: Four Short Courses in Harmonic Analysis, Applied and Numerical Harmonic Analysis (ANHA), Birkhäuser Verlag (2009), 1 - 49.
- B. Forster and P. Massopust, Statistical Encounters with Complex B-Splines, Constr. Approx. 29 (2009), 325 - 344.
- P. Massopust, Double Dirichlet Averages and Complex B-Splines, Proceedings of Sampta 2009.
- B. Forster and P. Massopust, Multivariate Complex B-Splines, Dirichlet Averages and Difference Operators, Proceedings of Sampta 2009.
- B. Forster, P. Massopust, Some Remarks about the Connection between Fractional Divided Differences, Fractional B- Splines, and the Hermite-Genocchi Formula, International Journal of Wavelets, Multiresolution and Information Processing, Vol. 6, No. 2 (2008), 279 - 290
- P. Massopust, P., D. Larson, Coxeter Groups and Wavelet Sets, Contemporary Mathematics, Vol. 451, 187 - 218, 2008
- B. Forster, P. Massopust, Multivariate Complex B-Splines, Proceedings of SPIE, Wavelets XII, Vol. 6701, 670109-1 – 670109-9, 2007
- P. Massopust, Multiwavelets: Some Approximation-Theoretic Properties, Sampling on the Interval, and Translation Invariance, Harmonic Analysis and p-Adic analysis, Eds. N. M. Chuong et al., World Scientific Publishing Co., 37 - 57, 2007
- P. Massopust, A Class of Solutions to Maxwell's Equations in Matter and Associated Special Functions, Advances in Deterministic and Stochastic Analysis, Eds. N. M. Chuong et al., World Scientific Publishing Co., 131 - 175, 2007

## Recent Grants and Sponsored Research

- BayFor (Bayerische Forschungsallianz) Grant for the initiation or immersion of international research collaborations: Efficient representations of multivariate signals, Jan.--Dec. 2015.
- DFG (German Research Foundation) Grant: Splines of Complex Order, Fractional Operators, and Applications in Signal and Image Processing, 2014--2016.
- Start-Up Grant for Cooperation between EuroTech Universities, Technische Universität München, Office of the President, 2012--2014.
- VolkswagenStiftung: Summer School on New Trends and Directions in Harmonic Analysis, Approximation Theory, and Image Analysis, 2007.

## Recent and Forthcoming Invited Conference and Workshop Presentations

- IM-Workshop on "Applied Approximation, Signals and Images," Bernried, Germany, February 2017.
- Centre International de Rencontres Mathématiques (CIRM), "Multivariate Approximation and Interpolation with Applications," Marseille, France, September 2016.
- 4th Dolomites Workshop on "Constructive Approximation and Applications," Alba di Canazei, Italy, September 2016.
- IM-Workshop on "Applied Approximation, Signals and Images," Bernried, Germany, February 2016.
- AMS Special Session on "Ergodic Theory and Dynamical Systems," AMS Annual Meetings, San Antonio, U.S.A., January 2015.
- International Conference on New Directions in Fractal Geometry, The Australian National University, Canberry, Australia, November 2014.
- International Conference Numerical Analysis and Applied Mathematics 2014, Minisymposium on Fractal Analysis and Harmonic Analysis, Rhodes, Greece, September 2014.
- Fifth International Conference on Computational Harmonic Analysis, Nashville, Tennessee, May 2014.
- International Conference on Fractals and Wavelets, Rajagiri School of Engineering & Technology, Kakkanad Cochin, Kerala, India, November 2013.
- CIMPA 2013, New Trends in Harmonic Analysis, Mar del Plata, Argentina, August 2013.
- AMS Special Session on "Harmonic Analysis of Frames, Wavelets, and Tilings," University of Colorado, Colorado, April 2013.
- Gesellschaft für Angewandte Mathematik und Mechanik (GAMM 2013), Mathematical Image and Signal Processing, Novi Sad, Serbia, March 2013.
- European Intensive Course on Complex Analysis, its Generalizations and Applications, Universidade de Aveiro, Portugal, March 2013 (three two-hour lectures).
- International Conference on Advances on Fractals and Related Topics, Chinese University of Hong Kong, China, December 2012.
- International Conference Numerical Analysis and Applied Mathematics 2012, Kos, Greece, September 2012 (two presentations).
- International Workshop on Operator Theory and Applications, University of New South Wales, Sydney, Australia, July 2012.

## Current Collaborations

- University of Newcastle
^{}, Newcastle, Australia - Technical University Denmark (DTU)
^{}, Copenhagen, Denmark - Universität Passau
^{}, Passau, Germany - The Australian National University
^{}, Canberra, Australia - University of St. Thomas
^{}, St. Paul, USA - DePaul University
^{}, Chicago, USA - Vanderbilt University
^{}, Nashville, USA

## Short and Minicourses, Invited Lecture Series

- Splines and Fractals in Approximation and Interpolation Theory, two-week long GIAN (Global Initiative of Academic Networks) lecture series, IIT Madras, India, July 2016, sponsored by the Government of India.
- Wavelet Sets, Affine Weyl Groups, and Fractal Surfaces (three two-hour invited lectures), $18^{\textrm{th}}$ European Intensive Course on Complex Analysis, its Applications and Generalizations, Universidade de Aveiro, Portugal, March 2013.
- Inverse Problems in Pipeline Inspection (one-hour invited lecture), AMS Short Course The Radon Transform and Applications to Inverse Problems, organized by G. \'{O}lafsson und T. Quinto, sponsored by the American Mathematical Society, Atlanta, Georgia, January 2005.
- Multiwavelets and their Applications (five-day mini-course), invited and sponsored by the Alleghany Section of the Mathematical Association of America, Meadville, Pennsylvania, Juni 1997.
- An Introduction to Fractal Functions and Fractal Surfaces and Their Connection to Wavelet Theory (three-day course), invited and sponsored by the Mathematical Association of America, San Francisco, California, January 1995).

## Teaching

### Summer Term 2016

- Elements of the Theory of Distributions
- Fourier and Laplace Transforms
- Workshop: Iterated Function Systeme and Fractals

### Past Terms

- Elements of the Theory of Distributions (Winter Term 2014/2015)
- Hauptseminar: Models for Evolutionary Dynamics (with Prof. Dr. Ch. Kuttler and Dr. J. Perez-Valezquez) (Summer Term 2014)
- Higher Mathematics 3 for Electrical Engineering (MA9403) (Winter Term 2013/2014)
- Fractal Geometry (Winter Term 2010/2011, Summer Term 2013)
- Complex Function Theory II (Winter Term 2009/2010, Winter Term 2012/2013, Winter Term 2015/2016)
- Lie Groups and Algebras (Summer Term 2012)
- Splines (Summer Term 2011)
- Hauptseminar: Mathematical Methods for Image Processing - Inverse Problems (Summer Term 2011)
- Differential Forms (Winter Term 2007/2008, Summer Term 2010, Winter Term 2011/2012, Summer Term 2015)
- Hauptseminar: Function Spaces (Winter Term 2009/2010)
- Meromorphic Functions and Riemannian Surfaces (Summer Term 2009)
- Proseminar: A Polynomial Approach to Linear Algebra (Winter Term 2008/2009)
- Topology (Summer Term 2008)
- Interpolation and Approximation with Splines and Fractals (Summer Term 2007)
- Proseminar: Complex Function Theory in the Plane and in Space (Summer Term 2007)
- Hauptseminar: Image Analysis (Winter Term 2006/2007)